A variable assignment, sometimes called a variable assignment function, is a crucial interpretation in formal languages for first-order or higher-order…
The upward Löwenheim–Skolem theorem states that if a first-order theory has an infinite model, it has models of arbitrarily large…
A substitution instance is the result of replacing variables in a well-formed formula with other formulas. Each variable must be…
The Skolem paradox highlights a contradiction between intuition and the Skolem-Lowenheim theorem. It shows that countable models can exist for…
A fundamental theorem in first-order logic. It asserts that if a theory has an infinite model, it possesses models for…
Satisfaction in model theory describes the relationship between a structure and a sentence, where the structure makes the sentence true…
Hilary Putnam's argument challenges how we understand reference and truth. It suggests semantic externalism can lead to skepticism about the…
Objectual quantifiers are a type of quantifier in formal logic that specifically refer to objects within the domain of discourse,…
A non-standard model adheres to a theory's axioms but possesses unintended properties. It's crucial for demonstrating a theory's consistency and…
Model theory is a branch of mathematical logic exploring the connections between formal languages and their meanings in mathematical structures.…